Stylianos Perrakis

Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs

By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option. A tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put. These results jointly impose tight upper and lower bounds on the implied volatility.

Option pricing and replication with transaction costs and dividends

This paper derives optimal perfect hedging portfolios in the presence of transaction costs within the binomial model of stock returns, for a market maker that establishes bid and ask prices for American call options on stocks paying dividends prior to expiration. It is shown that, while the option holders optimal exercise policy at the ex-dividend date varies according to the stock price, there are intervals of values for such a price where the optimal policy would depend on the holders preferences. Nonetheless, the perfect hedging assumption still allows the derivation of optimal hedging portfolios for both long and short positions of a market maker on the option.

Derivative Asset Pricing with Transaction Costs: An Extension

This paper examines the optimal perfect hedging (super-replication) of an option by a cash-plus-riskless asset portfolio within the context of the binomial model. The cases discussed here were not covered by the earlier studies of Boyle and Vorst (1992) and Bensaid, Lesne, Pagès and Scheinkman (1992). It is argued that these cases are empirically important, and that there is some indication that they are encountered very often in practice in the Swiss options market. A new algorithm is developed to compute the option price lower bound (bid price) for such cases. It is then shown that, for most such cases, the portfolio hedging the short call when replication is not optimal coincides with the Merton (1973) lower bound.

Capacity and Entry Under Demand Uncertainty

This paper examines the decision to enter into a sector dominated by a monopoly if demand is random at entry time. Given a two-period world, the monopolist enters initially and enjoys an uncontested monopoly for one period, while the entrant may enter and compete during the second period. Demand is random one period earlier and independently distributed in both periods and entry corresponds to an irreversible capacity choice, made under certain demand. All other production decisions take place after demand has been revealed. Risk-neutrality is assumed on both sides. If entry occurs then there is a Cournot duopoly in the second period. It is shown that concurrently with this Cournot production game, there is a separate Stackelberg-type game with capacities as decision variables. Entry-deterrence conditions are derived under general demand and cost assumptions. It is shown that demand uncertainty changes several of the results of similar certain demand models.

Minimum Quality Standards, Entry, and the Timing of the Quality Decision

This paper examines the effects of the imposition of minimum quality standards (MQS) on a vertically differentiated natural duopoly with free entry. It is shown that the welfare effects of MQS are crucially dependent upon the timing of the quality choice with respect to the decision to enter the market. If irreversible decision to enter is taken without pre-commitment to a specific quality level then a welfare improving MQS always exists. If, however, a firms product quality must be decided prior to entry then a MQS is either redundant or counterproductive, since it can induce a monopoly.

Option pricing : real and risk-neutral distributions

The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.

The American put under transactions costs

Abstract This paper examines the optimal super-replication of American put options with physical delivery of the underlying asset, such as stock options, by means of a stock-plus-riskless asset portfolio. The framework of the analysis is the binomial model with proportional transactions costs on stock transactions. The paper extends the model for European options, originally presented in Merton (Geneva Papers Risk Insurance 14 (1989) 225) and Boyle and Vorst (J. of Finance 47 (1992) 271), and generalized in Bensaid et al. (Math. Finance 2 (1992) 63). The optimizing framework of this latter study is adapted to put options held by investors and perfectly hedged by a market maker, and to put options written by investors and both held and hedged perfectly by a market maker. It is shown that a unique optimal super-replicating portfolio exists at every node of the binomial tree for the long option, as well as for the short option when transactions costs are low.

Moment Inequalities For A Class Of Single Server Queues

AbstractThe limiting behaviour of the single server queue is discussed for a general class of inter-arrival distribution functions of practical interest. New upper and lower bounds are derived for the first order measures (expected waiting time, queue size, etc.). Also presented are some numerical results on the influence of the inter-arrival and service time third moments upon the first- and second-order measures.

Valuing Catastrophe Derivatives Under Limited Diversification: A Stochastic Dominance Approach

We present a new approach to the pricing of catastrophe event (CAT) derivatives that does not assume a fully diversifiable event risk. Instead, we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives. Based on this approach, we derive values for a CAT option and a reinsurance contract on an insurer’s assets using recent results from the option pricing literature. We show that the assumption of unsystematic event risk seriously underprices the CAT option. Last, we present numerical results for our derivatives using real data from hurricane landings in Florida.

Free entry may reduce total willingness-to-pay1

Abstract In a natural oligopoly with quality commitments, entry accommodation may induce an incumbent to adopt a lower quality relative to a protected monopolist. Due to quality distortion a protected monopoly may be welfare superior to a duopoly even absent cost considerations.